Human Capital, Productivity and Growth
by
Audra Bowlus, Haoming Liu and Chris Robinson
Working Paper # 2005-2 September 2005
CIBC Working Paper Series
Department of Economics Social Science Centre
The University of Western Ontario London, Ontario, N6A 5C2
Canada
This working paper is available as a downloadable pdf file on our website http://www.ssc.uwo.ca/economics/centres/cibc/
HUMAN CAPITAL, PRODUCTIVITY AND GROWTH
Abstract
In this paper new estimates of human capital prices and quantities, taking into accounttechnological change in human capital production and endogenous education choice, arepresented for both Canada and the United States. The implications of the estimates for thesources of growth are examined. The most striking result is that adjusting the labour input forquality increases reduces the contribution of MFP growth in standard of living growth to zero.The largest part of this quality increase is not due to composition changes but instead totechnological change in human capital production. Since most attempts at adjusting the labourinput for quality changes only deal with composition, they cannot capture a large part of thequality change. The results suggest that technological improvement in human capital productioncould be the major source of standard of living growth in the last few decades.
Audra Bowlus*, Haoming Liu** and Chris Robinson*
*University of Western Ontario
**National University of Singapore
August 2005
__________________________________________*Chris Robinson is the CIBC Chair in Human Capital and Productivity and Audra Bowlus isCIBC Fellow in Human Capital and Productivity, both at the University of Western Ontario. Thisresearch is supported by the CIBC Human Capital and Productivity Project. We have benefitedgreatly from discussions with Lance Lochner.
1 See Willis (1986) for a survey.
2
1 Introduction
The flow from human capital is by far the most important input in the world economy.
The estimated share of labour in the United States and most of the OECD countries, for example,
is about two thirds. Human capital theory has been the basis of a huge literature studying the
determination of earnings since the seminal work of Becker (1964), Ben Porath (1967), Mincer
(1974) and many others.1 There is by now quite general agreement that human capital plays a
significant role in the determination of living standards. However, assessing the contribution of
human capital to output, living standards and growth is hampered by serious conceptual and
measurement problems, especially for international comparisons and for secular analyses over
several decades. In this paper we argue that a major omission in the literature has been to ignore
technological change, broadly interpreted, in the human capital production functions that
characterize a country’s education and on the job-training system. This has resulted in a serious
under-estimate of the growth of the labour input when conventional measures are used, and
conversely a large over-estimate of the growth of total factor productivity (TFP). Using a new
approach that takes technological change into account, we find that growth in the average levels
of human capital, not TFP, accounts for the increase in living standards in Canada and the United
States since 1975.
Since human capital is not directly measurable, a variety of approaches to measurement
have been taken in the literature. Most of these are based on what in the original human capital
models are more appropriately interpreted as inputs into the human capital production function
rather than the output. For example, a common measure of general human capital is years of
schooling. Refinements of this take into account work experience - usually in the form of some
2For example, the OECD report comparisons of a such a measure, designated A1, which thepublication characterizes as “traditionally used to proxy the stock of human capital” Education at aGlance - OECD Indicators, OECD 1998, p. 7.
3The issue of internationally comparable human capital measures that takes into account qualityvariation across country has received a great deal of attention. Barro and Lee (1993, 1996), for example,constructed measures of schooling years, designed to be internationally comparable, but stressed that themeasure of years did not take into account quality differences. Hanushek and Kim (1995) and Hanushekand Kimko (2000) use international test score data to address the issue of schooling and labour forcequality. Coulombe, Tremblay and Marchand (2004) utilize data from the International Adult LiteracySurvey, and argue that human capital measures based on these data are superior to years of schoolingmeasures normally used in international growth regressions. However, this literature pays little attentionto the issue of quality variation over time within countries, or to the identification or interpretationproblems that occur if human capital is heterogeneous.
3
measure of total accumulated time at work. For international comparisons, often the adopted
procedure is to compare the fraction of the relevant populations with various levels of education.2
At the most basic level, this methodology faces the major problem of aggregating workers of
different levels of education. This is sometimes avoided by choosing a measure such as the
fraction of the population who have graduated high school (for comparison across developing
countries) or the fraction of the population with post-secondary education (for comparison across
developed countries). However, this can result in misleading conclusions. According to the latter
measure, Canada has higher per capita human capital than the United States. However, the
United States has a higher fraction of the population with a university degree. If this measure was
used instead of the fraction with post-secondary education, the ranking would be reversed. For a
variety of important contexts, a better measure of human capital is needed. A better measure is
also needed to answer some of the most important questions in the current literature on wages,
productivity and growth.3
Several countries have attempted to get better measures of human capital by refining the
construction of their aggregate labor input indices, previously measured by aggregate labor hours,
to take into account changes in the composition of the labor force. The rapidly increasing average
education levels in the workforce was a major reason for this initiative. However, these measures
do not take into account endogenous schooling decisions, or more importantly, technological
4
change in the production function for human capital itself. As a result, they fall a long way short
of measuring the actual increase in the labour input. Our estimates show a substantial increase in
human capital due to technological change that the conventional composition adjusted measures
cannot capture.
Measuring technological change in human capital production functions presents special
problems because of the difficulty of measuring the output. In Bowlus and Robinson (2004), a
technological improvement is measured by the estimated increase in human capital quantity
associated with any observed level of education or job market experience. The interpretation of
technological change is a broad one. In particular, this technological change should not be
narrowly interpreted as the technological means of conveying a given set of information from a
teacher to a student. Obviously, the information conveyed changes over time. Presumably the
amount of “physics task” that a physics graduate from a given point in the initial human capital
endowment distribution in the 1966 birth cohort can do is much larger than that of the graduate
from the 1946 cohort from the same point in the distribution mainly because of the advanced
physics information conveyed rather than a better technology of conveying the same instruction
that the 1946 birth cohort individual received.
The data used for the paper come from the United States and Canada. The data from these
countries are broadly comparable. The two countries are quite similar in many ways, but for the
issues raised in this paper, they provide an excellent contrast for comparison purposes. In
particular, the differential between average wages of skilled workers and unskilled workers has
taken a quite different path in the two countries in the last few decades. In addition, there has
been a widening gap in the standard of living between the countries.
Section 2 discusses identification issues in homogeneous and heterogeneous human
capital models, while Section 3 describes and compares the data sources for the two countries.
The estimated price series for the United States and Canada are reported in Section 4. The labour
input price declined substantially in both countries until the early 1990s. This decline is much
5
larger than is apparent in composition adjusted aggregate wage series. In the recovery from the
early 1990's recession, the series for the two countries diverge. The price in the United States
began a substantial upward trend, while in Canada the price decline continued. By 2000, this
divergence produced a gap of 13 percentage points in the labour input price in the two countries.
Over the same period, the average Canadian worker suffered a substantial loss in standard of
living relative to the average United States worker, in large part due to receiving a lower price for
his/her human capital relative to United States workers.
Section 5 presents estimates of the quantity of human capital in Canada and the United
States. The series show faster growth in efficiency units for the United States. At the per worker
level the difference in growth rates in efficiency units for the 1980-2000 period was relatively
modest. In the United States, per worker efficiency units grew by 37.42% compared to 31.58% in
Canada. This contributed about one third to the 18% relative loss in standard of living for the
average Canadian worker, while the remaining two thirds was due to the declining price of
human capital in Canada compared to the United States following the early 1990's recession.
Section 6 compares these labour input estimates with standard composition adjusted
aggregate labour input measures, including series calculated by Jorgenson and the Bureau of
Labor Statistics (BLS) for the United States and Statistics Canada for Canada. The comparisons
show that conventional composition adjusted measures substantially underestimate the labour
input. In both countries the composition adjustments result in estimated rates of growth in the
labour input in that are 36-40% higher compared to unadjusted hours. However these
composition adjustments fall a long way short of the growth in efficiency units. In both countries,
the rate of growth of efficiency units is about 40% faster than the rate of growth of composition
adjusted hours. In the United States the growth rate of efficiency units is 90.11%, which is ten
percentage points higher than Canada’s rate of 79.43%. Roughly two thirds of the difference is
due to faster growth in hours in the United States and one third to a faster growth in efficiency
units per hour. Only a very small part of the difference in efficiency units per hour is due to
composition differences. Thus, BLS style comparisons cannot identify the main source of the
4See Manuelli and Seshadri (2005).
6
difference in efficiency units per hour across the two countries.
The substantial underestimate of the aggregate labour input in conventional measures has
important implications for TFP or multi-factor productivity (MFP) estimates which use these
labour input measures. These are discussed in Section 7. The estimates suggest that most, if not
all, of the BLS estimated growth in MFP in the private business sector from 1975 to 2001 is due
to the undercount of the increase in the labour input. Similarly, for Canada over the period 1980-
2000, the under-estimate of the labour input using standard composition adjusted measures is the
source of all the estimated MFP growth for the period. Using the quality adjusted labour input,
MFP contributes nothing to changes over the period in living standards in the two countries. This
dramatically reduced role for MFP when the quality of human capital is taken into account is also
found in a recent study of cross country variation in wealth.4 Finally, some conclusions and
discussion of future work are given in Section 8.
2 Identification Issues: The Price and Quantity of the Human Capital
Input
In standard human capital models with competitive firms the hourly wage is the product
of a price and a quantity:
wit = 8tEit (1)
where Eit is the amount of human capital supplied to the firm (number of efficiency units) by
worker i in time period t, and 8t is the rental price paid for renting a single unit of human capital
(the price of an efficiency unit). The hourly wage is observed, but its two components are not.
This is the fundamental under-identification property of human capital models.
5See, for example, Krusell, et. al. (2000).
7
In a homogeneous human capital model there is a single price, 8, and wages differ across
workers in any given time period because of differences in the amount of (homogeneous) human
capital they are supplying. Over time a worker’s wage could change either because of a change in
the quantity of efficiency units he/she supplied, or because of a change in the efficiency units
price. Over time, relative wages between any two observable “types” of workers reflect only
relative changes in quantity supplied by each type since there is a single price. This is the main
consequence of the efficiency units approach in a homogeneous human capital model.
In the heterogeneous human capital models, an efficiency units approach is retained
within some exogenously defined worker “type” (e.g. college degree) but is abandoned across
types.5 With two worker types (e.g. college and non-college) there are two factors and two prices
with wages given as follows (suppressing the subscripts for convenience):
wa = 8aEa and wb = 8bEb
where 8a and 8b are the prices of efficiency units of type a and b respectively, and Ea and Eb are
the number of efficiency units of type a supplied by a type a worker, and the number of
efficiency units of type b supplied by a type b worker, respectively. Within type, the wage
implications are the same as the homogeneous human capital model. For relative wages across
types the implications are potentially different. Since there are now two prices, changes in
relative wages between two types reflect changes in relative quantities Ea/Eb and changes in
relative prices 8a/8b .
The analysis in this paper uses a homogeneous human capital model in preference to a
heterogeneous model. The benefits of a homogeneous human capital model for this type of
aggregate level study are many. The simplicity and ease of aggregation are a major advantage for
the purposes of comparing human capital stocks across time or countries or assessing the
8
contribution of human capital to growth. The single price feature is a major advantage in
providing an elegant solution to the problem of defining an aggregate wage. The single type
feature provides a similarly elegant solution to the problem of defining an aggregate quantity.
Homogeneous human capital models are, in fact, implicitly or explicitly used in many aggregate
studies, especially those concerned with growth, where a single aggregate labour input is used.
In recent micro level studies, heterogeneous human capital models have been prominent
in the debate over skill-biased technological change and rising inequality in the United States.
These heterogeneous models have several drawbacks for the type of aggregate analysis
conducted in this paper. If human capital is heterogeneous and the types are observationally
identifiable by, say, education level, there is in fact little to be gained by arbitrarily aggregating
the different types. Indeed, since the types are different factors of production, from a production
function point of view the types can no more be sensibly added than adding kilowatts of
electricity and hours of “unskilled” labour. There is no common unit for the addition. An
aggregate level analysis can be carried out with a heterogeneous model, but without a meaningful
aggregate labour input.
One reason for the popularity of heterogeneous human capital models is the apparent
inconsistency of the homogeneous model with the evidence in the United States of a rising skill
premium. However, evaluating this evidence in light of the fundamental under-identification of
human capital models, Bowlus and Robinson (2004) argue that a single price model, based on a
homogeneous human capital model amended to take into account education selection and
technological change in human capital production functions, is a very good approximation. In
fact, this homogeneous model with technological change is consistent with the overall skill
premium pattern, including the pattern by cohort within heterogeneous type. The standard
heterogeneous model that identifies the skill price ratio by assuming no technological change or
selection is consistent with the time path of the observed cross section wage ratio by skill in the
6See Card and Lemieux (2001) for the cohort patterns in the United States, and the difficultiesthe heterogeneous model faces in explaining the Canadian data.
9
United States, but not with the cohort pattern.6 Thus, the aggregation advantages of a
homogeneous human capital model can be retained without any conflict with the evidence on
skill premia.
The identification of the prices and quantities of human capital is a difficult problem in
both homogeneous and heterogeneous human capital models. In heterogeneous human capital
models it is implicitly solved by assuming that the quantities of human capital associated with
any observed education level at any point in time are the same. This permits the identification of
the skill price ratio from the wage ratio. It also permits the identification of (changes in) the
quantities from the hours supplied at any observed education level. However, as noted earlier,
this rules out both education selection and technological change in human capital production.
Since major quality improvements due to technological change have been found for capital
inputs such as computers, it is surprising that it is generally ruled out for the labour input. In the
computer case, estimates of the quality improvements are relatively easy to obtain since the
efficiency units in computers are directly measurable. Suppose instead that they were not in fact
directly measurable, and that only price information, etc., was available. If the standard
identifying assumption used in the heterogeneous human capital model was applied to the
computer input, using the cost of the inputs that went into its manufacture, the price paid for it, or
the size of the “box”, it would clearly be a very bad assumption.
Bowlus and Robinson (2004) consider two identification methods: the “standard unit”
method, which can be applied under certain conditions to identify prices and quantities over time
within a homogeneous human capital model, and the “flat spot” method which can be used with
either homogeneous or heterogeneous models. In principle, the simplest approach to
identification in a homogeneous human capital model is to find an observable “standard” unit of
human capital that is the same across time. In that case, observing the wage paid for a standard
unit at different points in time identifies the price change. Given the homogeneous human capital
10
assumption, this price can then be applied to any worker’s wage to infer the quantity of human
capital. This is similar to the notion of finding a time invariant common unit for computers. The
solution in the computer case was to assume that the common unit that represents the factor
provided by all computers is calculations per second. That is, calculations per second are the
efficiency units. The relevant price is the price of a “standard” computer defined as having a
given number of calculations per second.
Given the assumption of the common unit, the identification problem in the computer
case is made very simple by the fact that computations per second can be observed so it is not
necessary to actually observe “standard” computers over time to identify the relevant price. In the
human capital case it is necessary to observe a standard unit over time because efficiency units
are not directly observed. In principle, an ideal standard unit would be a group of workers, drawn
from the same region of the initial human capital endowment distribution in each period, who
made no further investment in human capital. In practice, a group with the lowest exposure to
human capital production functions, and the least addition to their initial human capital
endowment has to be used.
The flat spot method, proposed in Hechman, Lochner and Taber (1998), is based on the
fact that most optimal human capital investment models have the feature that at some point in the
working life-cycle, optimal net investment is zero. If there is a period of years in which this
occurs, the human capital of a given cohort over those years is constant by assumption. That is,
there is a flat spot in the human capital life-cycle profile. Observing the changes in average
wages for the cohort over the flat spot, therefore, identifies the human capital price changes.
Provided such flat spots exist, this method can be used with any skill group to identify skill
prices.
3. Data Sources
The data source for the United States is the March Current Population Surveys (MCPS)
7The closest equivalent repeated cross section data sources for Canada come from the Survey ofConsumer Finances (SCF). This survey was held every year from 1982 to 1998 except 1984 andrepresents an annual survey measuring previous years earnings in a way similar to the MCPS.Unfortunately, there are several serious problems in the Canadian data that do not occur in the MCPS.The most serious problems are the non-contemporaneous measures of hours and earnings and a majorbreak in the education series. The survey measures total earnings from wages and salaries for thepreceding year and records the number of weeks worked in the same (preceding) year. However, themeasurement of usual hours per week refers to the reference week of the survey, rather than thepreceding year. The education questions changed significantly between the 1988 and 1989 earningsyears, resulting in a sharp change in the percentage of individuals recorded in post-secondary education.Gu et. al. (2002) argue that the census education measures are preferable in this regard to the SCFmeasures and use the census for the Statistics Canada series on a composition adjusted labour inputseries for 1961-2000.
11
for 1976 to 2002. The earnings data are earnings from wages and salaries from the calender year
preceding the survey, covering 1975-2001. The earnings data were confined to paid employees
by restricting the sample to those for whom the class of worker on the longest job in the year
preceding the survey was a private or public paid employee. An adjustment was made to correct
for top-coding. Paid employees were distinguished according to observed education level. Prior
to the survey year 1992, the MCPS education measure was the number of years of schooling
completed. After January 1992, actual degrees and diplomas were recorded. This break in the
series was examined in detail in Jaeger (1997), using a matched panel of respondents that
answered both forms of the education questions. Jaeger derives a recoding scheme to produce
approximate consistency in four categories: dropouts, 12th grade, some college and college
graduates.
The Canadian data set is derived from the public use samples from the censuses for 1981,
1986, 1991, 1996 and 2001.7 The census contains measures of total wage and salary earnings
and total weeks worked in the previous year, as in the MCPS for the United States. There is no
measure of usual hours in the previous year, but it is possible to identify which individuals were
working mainly full time in the previous year, so an hourly wage rate can be constructed. The
United States series was constructed using data on paid employees. It is not possible to identify
class of worker status on the longest job in the preceding year in the Canadian data. The
restriction to paid employees is imposed instead by requiring no self-employed earnings. Given
8The census documentation makes it clear, however, that “highest level of schooling” should notbe interpreted in a strictly hierarchical sense because of the difficulties of ranking various forms of “post-secondary” education categories. The census also records the highest grade attended whether or not thiswas the highest level of schooling. Examination of this, together with the highest level of schoolingshows a strong pattern of “leap-frogging” in the highest level of schooling variable based on the post-secondary information. That is, for example, there is a substantial number of individuals whose highestgrade was as low as 5-8 that, on the highest level of schooling variable, rank above individuals whograduated from high school. This leap-frogging is due to the receipt of post-secondary certificates belowthe university degree level. Details of the Canadian categories are given in the Appendix.
9It raises the more general problem of formal and informal training after elementary or highschool. If a worker, A, with a grade 10 education works for a firm that trains its workers “in-house” iscompared to a worker, B, also with a grade 10 education but whose firm trains its workers at an outsideoperation that may or may not grant a certificate, should worker B be rated as having more education? Ifthe training was the same, the workers would have the same human capital. If this kind of roughlyequivalent post-school training increasingly took place outside firms the fraction with post-secondaryeducation would increase without any increase in human capital and the apparent wage gain from the
post-secondary education would be zero.
12
the small size of the self-employed population and the relatively small contribution of self-
employed earnings to the total earnings of workers in the United States whose longest job was
not self-employed, it is assumed that this difference in definition has a negligible effect on
differences in mean earnings for paid employees. As for the United States data, an adjustment
was made for top-coding, though in the Canadian data the incidence of top-coding is very small.
The education categories in the Canadian censuses for 1981-2001 are based on grades
attended and degrees and diplomas received, like the United States surveys after January 1992,
and are consistent over time. The detailed categories in the “highest level of schooling” variable
can be divided into four groups that broadly correspond to Jaeger’s four groups for the United
States: dropouts, high school graduates, some post-secondary, and BA degree or higher.8 The
dropout category presents some problems of comparability. Canada currently has a high fraction
of individuals with some post-secondary education obtained outside university. This fraction has
changed substantially over time. Since much of this education does not require a high school
grade level above 10, let alone high school graduation, it is not clear how it should be treated.9
The dropout group in the United States has no post-secondary education. The dropout group used
13
for Canada imposes this requirement; the precise definitions for Canada are given in the
Appendix.
4 Estimates of Human Capital Prices for the United States and Canada
This section presents and compares estimates of human capital price series for the United
States and Canada based on three alternative methods. The standard unit method is applied to the
young dropout group in each country. The flat-spot method is applied to relevant age ranges for
the dropout group in each country to estimate price series for the least skilled, and to the group
with a BA degree or higher to estimate skilled price series for comparison. Detailed discussion of
the computation methods is given in Bowlus and Robinson (2004).
The standard unit approach requires the group corresponding to the standard unit to be
drawn from the same region of the initial endowment distribution across cohorts. The choice of
standard unit involves a number of tradeoffs, discussed in detail in Bowlus and Robinson (2004).
The education level for this group should be the lowest of the categories - the dropouts. The first
check on potential biases with the standard unit method is to see if the fraction of dropouts in
each birth cohort that supplies the standard unit group across the years of the sample is the same
over time. As Figure 1 shows, this is true for the United States; for Canada, however, this
fraction declines over time.
The pattern in Figure 1 for both countries is a strong decline until the post-war birth
cohorts. At this point, however, the patterns diverge. The relevant cohorts for the price series that
can be constructed for Canada, are the 1958 - 1973 birth cohorts. Between the 1958 and 1973
cohorts, there is a drop in the fraction of dropouts in the cohort from 25.17% to 16.97%,
representing a decline of about one third. In the United States, by contrast, the fraction over the
relevant cohorts, beginning in 1955, is constant. Assuming a positive correlation between
schooling level choice and initial human capital endowment, the decline over time in the cohort
dropout fraction exerts a downward bias in the estimated price series for Canada based on the
14
standard unit method. The constant fraction of dropouts in the United States across cohorts
suggests that this potential bias is not present for the estimated standard unit price series for the
United States.
A second check on the validity of the assumptions for the standard unit method is an
examination of whether the variance of log wages for the standard unit group is constant over
time. Figure 1 shows that for the United States the fraction in the relevant cohorts is the same
over time. If this represents the same drawing from the initial endowment distribution, both the
mean and variance of efficiency units, or the log of efficiency units, should be the same across
cohorts. The variance of wages is proportional to the square of the efficiency units price, but the
variance of log wages is equal to the variance of log efficiency units. Figure 2 shows the variance
of log wages for the relevant United States birth cohorts. While there is some noise, there is no
evidence of any change in the variance that would violate the standard unit assumption for the
United States data.
Table 1 presents the estimates for the United States obtained from all three approaches:
the standard unit method using dropouts aged 18-20 in the earnings year, and the flat spot method
applied to both dropouts and the university group (BA degree or higher). The flat spot method
was implemented for both dropouts and those with a BA degree or higher using pairs of adjacent
years and pooling the estimates of each pair assumed to be in a ten year flat spot region. An
important result is that the flat spot series for a representative dropout group, using ages 48-57,
and the university series, using ages 53-62, are very close to one another. The correlation
between the series is .9455. The main requirement for the flat spot analysis is that the flat spot is
correctly identified. General human capital theory suggests a flat spot towards the end of the
working life-cycle. Figure 3 shows that for the United States the flat spot method is relatively
insensitive to the age range chosen for the flat spot when the method is used on the dropout
group. This might be expected as a reflection of relatively flat life-cycle human capital profiles
for less educated groups. Figure 4 shows the sensitivity of the flat spot method applied to the
university group. While there is more sensitivity for the university group, the overall patterns are
15
the same.
Table 1 shows that the flatspot and standard units approaches produce closely related
series. These series from Table 1 are plotted for comparison in Figure 5. The only significant
difference is in the recovery after the 1981 recession where the standard unit approach indicates a
larger drop relative to the other series. This provides substantial evidence that the use of a single
price for human capital is a very good approximation. The credible regions for the flat spots
show surprisingly similar price series for the two extremes on the human capital spectrum - the
dropouts and those with a BA degree or higher. Since the dropouts leave school about 5 years
earlier than those with a BA degree or higher, the flat spot region is likely to occur at an earlier
age. The high correlation between the series based on the 48-57 region for dropouts and the 53-
62 age region for those with a BA degree or higher is consistent with this. In addition, the price
series using the standard unit approach is also similar. Despite the different paths of average
wages for dropouts and those with a BA degree or higher, this evidence indicates that, rather than
being due to different price paths for the two groups, it was due to different average efficiency
units paths.
The last column of Table 1 shows a final price series to be used in computing the quantity
series in Section 5. This is an average of the three series in Figure 5. For the overall change from
1975 to 2001, the average price series shows an 18% drop. The range of estimated overall
declines in Table 1 is 15% to 20%. This range in part reflects the uncertainty of the flat spot
range. For both the dropout and university groups, the earlier age group shows a smaller drop
relative to the later age group. This is expected from the typical theoretical profile for human
capital, where the later age group is either at a flatter part of the profile as it approaches the flat
spot, inducing less of an upward bias in the estimated price than the younger group, or is beyond
the flat spot, inducing a downward bias.
The price series for the United States shows a very strong decline to 1993 followed by a
recovery. The percentage drop from 1975 to 1993 is about 24% and the recovery reduces the
10A slightly older age group was chosen to minimize the problems of “leap-frogging” from thedropout to the post-secondary category over time in the Canadian data and results are presented for twoalternatives. The problem arises from the changes over time in who leap-frogs out of the Canadiandropout group into post-secondary education - potentially a highly selective process. Many of these post-secondary certificates acquired by individuals without high school graduation are obtained by age 22.Starting the standard unit from this age removes these individuals from the dropout group, minimizingselective changes that would occur from changes in leap-frogging over time.
16
overall drop over the 1975-2001 period to 18%. There is a particularly steep decline in the first
decade of almost 17%. This substantial decline to 1993 indicates a large increase in the supply
of efficiency units relative to demand over the period. Only by the mid 1990's does the upswing
in demand reverse the downward trend in the efficiency units price. It should be noted that this
price series is quite different from what would be obtained from a conventional composition
adjusted aggregate wage series. In particular, the price decline is much steeper than suggested by
aggregate wage series. Thus, estimates of behavioural responses to the labour input price based
on aggregate wage series are likely to be seriously biased.
The estimates for Canada are presented in Table 2. The standard unit group is similar to
that used for the United States.10 The Canadian data set is every five years instead of being
annual. A flat spot method, corresponding as closely as possible to the method used for the
United States, can be applied to the Canadian data set for the 1980-2000 period by following the
same five year cohort group across adjacent five year censuses, such that in both censuses the age
range of the cohort group remains within the ten year flat spot. The five year intervals may,
however, increase the measurement errors due to the synthetic nature of the cohorts.
The first two columns of Table 2 report standard unit estimates for Canada. As discussed
above, these are downward biased because of the decline in the cohort fractions in this group
over time, and subject to the leap-frogging problems that selectively remove dropouts into the
post-secondary group in a way that is difficult to detect with any precision. Inspection of the
Canadian series in Figure 1 suggests that the bias may be significant in the earlier part of the
series, as this shows the most rapid fall. The remaining columns of Table 2 report flat spot
estimates for both dropouts and those with a BA degree or higher for a variety of possible flat-
17
spot regions. The series are relatively insensitive to the choice of flat-spot region. Like the series
for the United States, there is also strong similarity for the series of the two extremes of human
capital levels. The correlation between the flat-spot series for the dropouts with flat spot region
age 49-58, and any of the BA degree or higher series is always well above 0.9. Thus the
evidence from Canadian data reinforces the evidence in Table 1 that a single price for human
capital is a very good approximation. Comparison with the standard unit series shows, as
expected, a downward bias in the standard unit estimates, especially in the earlier part of the
series.
The last column in Table 2 reports the series average that is used to compute efficiency
units in Section 5. Since the standard unit series for Canada suffer from potential bias problems,
they were omitted in the averaging. Instead, the series in the last column is the average of the
flat-spot series. Figure 6 compares the price series for Canada and the United States, normalizing
both series to 1 in 1990. Until the recovery from the recession in the early 1990's, both series
show a similar downward trend. Thereafter, the United States series shows a clear recovery in the
price, while the price in Canada continues to decline. In 2000, there is a gap of 13 percentage
points between Canada and the United States due to the continuing fall in the price in Canada
and the increase in the United States after 1993. The average Canadian worker suffered a large
loss in standard of living relative to the average United States worker. The price series in Figure
6 suggest that much of this was due to the relative decline in the price of human capital in
Canada.
5. Stocks of Human Capital in Canada and the United States
In this section, the efficiency units price series estimated in Section 4, are used to derive
the total supply of efficiency units in each country, and the per paid employee levels of efficiency
units by sex. Total efficiency units in any period t, are, by definition:
Nt = 3j Ejthjt
11This abstracts from discrimination. See the Appendix for adjustments required when there isdiscrimination.
12See Bowlus and Robinson (2005) for a discussion of the identification problems.
18
where Ejt are the efficiency units supplied per hour by worker j in period t and hjt are the hours for
which those efficiency units are supplied. All firms pay the same price, 8t, for hourly efficiency
units in period t, so the hourly wage paid to worker j is:
wjt = 8tEjt
and total period wage earnings for worker j are:
wjthjt = 8tEjthjt
hence Nt = 3j (wjthjt)/8t (4)
Thus to compute a total efficiency units series the total wage payments are simply divided by the
price series. For efficiency units for any sub-group, the relevant series can be computed using the
wage payments to the sub-group.11
Comparison of efficiency units across countries raises many difficult issues.12 However,
the growth of efficiency units may be compared. In Table 3, the growth rates for 1980-2000 in
wage and salary earnings and efficiency units per paid employee for Canada and the United
States are shown. For all paid employees, the growth rate in earnings from 1980 to 2000 was
29.07% in the United States compared to 8.91% for Canada. Most of this growth occurs over
1990-2000. Relative to the position in 1980, Canadian paid workers thus experience a decline in
standard of living compared to paid workers in the United States of 20%. A large part of this
decline is due to the difference across countries in the price path of efficiency units shown in
Figure 6. This is apparent in the columns reporting rates of growth of efficiency units for the two
countries. For the United States the growth is 45.54% compared to 38.22% for Canada. Over
19
1990-2000, the growth in efficiency units is, in fact, marginally higher in Canada. Thus, while
the relative standard of living decline is 20%, about two thirds of this is due to the different price
path (13%), and only one third to the different rates of growth in the amounts of human capital
supplied (7%).
For males, the growth rate in earnings from 1980 to 2000 is 21.88% in the United States
compared to 3.68% in Canada. The 1990-2000 period represents almost all of the growth in
earnings in both countries. Again, there is a large decline in standard of living for Canadian male
workers relative to those in the United States, of about 18%, with at least two thirds (13%) due to
the lower price for human capital in Canada in 2000. The per worker efficiency units for males
did grow faster in the United States (37.42%) compared to Canada (31.58%), but this accounts
for only one third of the decline in the relative standard of living. From 1990 to 2000, where the
price decline in Canada was 13% compared to zero in the United States, per worker human
capital actually grew marginally faster for males in Canada compared to males in the United
States. The pattern for females is similar. The primary difference is that the rates of growth in
efficiency units for females are about 25 percentage points higher in both countries. Overall, the
growth for females was somewhat higher in the United States (70.35%) compared to Canada
(63.35%), but in the most recent decade the rate of growth in Canada surpassed that of the United
States.
The total supplies of paid workers and efficiency units in the economies of Canada and
the United States are presented in Table 4. The rates of growth in the total paid worker
population for 1980-2000 are very similar in the two countries: 29.44% in the United States,
compared to 28.72% in Canada. The United States, however, has a larger growth in efficiency
units: 88.38% vs. 77.92%. In the most recent decade, the population of paid workers in the
United States grew considerably more than in Canada (13.91% vs. 9.22%), but efficiency units
grew at a similar rate in the two countries (35.78% vs. 34.25%). The breakdown by sex shows
that the faster growth in paid workers in the United States was due to the differential growth for
males. Both the number of male paid workers and total efficiency units increase at a faster rate in
20
the United States. Growth in the number of paid workers is 23.39% in the United States
compared to 18.20% in Canada. This is reflected in the faster growth in efficiency units for
males: 69.57% in the United States compared to 55.53% in Canada. For females , the population
growth from 1980 to 2000 was higher in Canada (42.19% vs. 36.47%), but this was not reflected
in a higher growth in efficiency units. Efficiency units grew at the same rate in both countries.
Most of the paid worker population growth for females in Canada occurred in the 1980s, largely
due to a faster increase in the employment rate for females in Canada.
As discussed in the Appendix, the computation of efficiency units for females depends on
the magnitude of wage discrimination against females and its path over time. In addition, the
change in per worker efficiency units are affected by the rise in female participation over time. In
Tables 3 & 4 the efficiency units are all calculated under the assumption of no discrimination.
The comparison across countries for males is not complicated by these issues, and is less affected
by different labour supply paths in the two countries over time. The sensitivity of the estimates of
rates of growth of the total labour input to alternative assumptions regarding discrimination is
considered further in the following section.
6. Comparison of Human Capital Quantity Series with Standard
Composition Adjusted Aggregate Hours Series
The quantity series presented in Section 5 are substantially different from conventional
series based on composition adjusted aggregate hours. Since the composition adjusted series
account for changes in the proportions of workers with different education levels in the labour
market, the differences between conventional series and those presented in Section 5 reflect the
effect of technological change in the production function for human capital. In general, the series
estimated in Section 5 show significant amounts of technological improvement. In this section,
the human capital quantity series, allowing for technological change, are compared with the most
well known composition adjusted series for the United States, and with similarly constructed
13Labor Composition and U.S. Productivity Growth, 1948-90. U.S. Department of Labor, Bureauof Labor Statistics, Bulletin 2426, December 1993.
21
series for Canada.
Aggregate Labour Input Measures for the United States
The BLS provides the main official composition adjusted series for the United States as
part of its Multi-factor Productivity Program. The motivation for the series is described in BLS
Bulletin 2426 (1993).13 Prior to this series, labour input had been measured by the total hours of
all workers. It was widely recognized that “the effective quantity of labor input does not rest
solely on the total number of hours worked by members of the U.S. labor force but also on
characteristics of the labor force.” (p. iii). Following the recommendations of a National
Academy of Sciences Panel to Review Productivity Statistics in 1979 the BLS developed a
weighted measure of total hours focusing on the skill level of workers as reflected in education
and job market experience levels. This measure is used in the construction of the BLS multi-
factor productivity index. It results in a substantially different interpretation of the path of multi-
factor productivity in the United States than estimates obtained using an unweighted aggregate
hours measure.
The BLS measure is described in detail in the BLS Handbook of Methods (1997), and in
BLS Bulletin 2426 (1993), which reported the first estimates. It is based on a Tornqvist chained
index of weighted hours of workers classified by skill and demographic characteristics. The
hours measures used in the original BLS Bulletin 2426 (1993) study for the period 1968-1990
were obtained from the MCPS. For the current series for the BLS Multi-factor Productivity
Program, hours are obtained mainly from the BLS Current Employment Statistics (CES)
program, based on establishment surveys. They are supplemented by data from the CPS and
other sources for groups not covered under CES. The weights are the shares of total
compensation for each type of worker classified by skill and demographic characteristics. They
are allowed to vary each year.
14See, for example, Chinloy (1980), Denison (1985) and Jorgenson, Gollop and Fraumeni (1987).
15Available at: http://post.economics.harvard.edu/faculty/jorgenson/papers/lqualprivate.xls
16The published Jorgenson series has 1996 as the base and was adjusted to 2000 to match thebase year for the published BLS series.
22
Prior to the development of the BLS measure, a number of authors had developed and
published composition adjusted aggregate hours series.14 The most well known current version of
these is the Jorgenson series for the United States private economy, 1977-2000.15 There are some
differences in the details of the methods and coverage, but the basic methodological approach is
the same for both the Jorgenson and BLS series, and the two series are very similar for the 1977-
2000 period. The series are given in Table 5. The first two columns show the aggregate hours for
the private economy. The coverage is a little broader for Jorgenson’s series, but the pattern is the
same. Overall growth in aggregate hours from 1977 to 2000 for the Jorgenson series is 53.39%
compared to 50.42% in the BLS series. The next two columns report the composition adjustment
factor with 2000 as the base.16 The adjustment factors for the Jorgenson and BLS series are
almost the same. The final three columns report the composition adjusted labor input. In the first
of these, the Jorgenson series is higher than the BLS series, despite the similar composition
adjustment factors, because of the wider coverage. The last two columns show that, when the
Jorgenson series is scaled to the BLS series in 1977, the two labour input series look almost the
same.
The growth in the labour input series that adjusts for composition is substantially higher
than the aggregate hours growth. Using the BLS figures in Table 5, the hours growth is 50.42%,
but the composition adjusted input growth is 66.68%. Thus, the changing composition
contributed almost one quarter of the total growth in the composition adjusted input. Since the
growth rate using composition adjusted hours is almost one third higher than when using hours,
the use of hours in constructing the MFP would substantially bias the change in the index over
this period. Adjusting hours for composition changes is clearly important. However, because it
ignores technological change in human capital production, and endogenous choice of human
23
capital investment, the composition adjusted series itself is subject to bias. In the presence of
technological improvement, composition adjustments to aggregate hours, like those of the BLS
or Jorgenson’s, will still underestimate the true labour input.
To estimate the magnitude of the bias for the United States, we use a single data set, the
MCPS, to construct three measures of the labour input: an aggregate hours measure, a
BLS/Jorgenson style composition adjusted aggregate hours measure, and the efficiency units
measure reported in Section 5. Comparisons between these three measures have a simple
interpretation within the efficiency units framework. The BLS measure uses a Tornqvist chained
index. Divide hours of labour into N skill groups where all members are the same “quality”, i.e.
the same efficiency units per hour. For the BLS these are groups based primarily on sex,
education and experience. Define the price of labour (average hourly wage rate) in group i at
year t, <it, implicitly as:
<it = Wit/hit
where Wit is total labour compensation in group i, in year t, and hit is the total number of hours.
Let Eit be efficiency units per hour for a member of group i. The construction of the Tornqvist
chain index of composition adjusted labour input used by the BLS is as follows. For group i the
ratio of the labour input in year t to the input in t-1 is by definition:
Li,t/t-1 = Eithit/Eit-1hit-1
In the BLS approach, there is an implicit assumption that there is no change in efficiency units
per hour within the group (Eit=Eit-1), so that
Li,t/t-1 = Eithit/Eit-1hit-1 = hit/hit-1
Aggregating across groups, the Tornqvist chained index (ratio) of the total labour input in year t
24
to the input in t-1 is given by weighting the ratios of the groups as follows:
Lt/t-1 = (Lt/Lt-1)= J(hit/hit-1)w(it) or ln (Lt/Lt-1) = 3wit ln(hit/hit-1)
where
wit = (Wit/(3Wit) + Wit-1/(3Wit-1))/2 = (<ithit/3<ithit + <it-1hit-1/3<it-1hit-1)/2
If Eit = Eit-1, this weighted sum of the approximate percentage growth in the hours of each group
is also a weighted sum of the approximate percentage growth in the efficiency units of each
group, where the total efficiency units of group i in period t are Nit = Eithit.
The BLS series from an initial period zero to t follows by chaining the ratios, Lt/t-1, to get
the change from zero to t:
)Lt/0 = Lt/t-1Lt-1/t-2....L1/0
so that the value in any period t is given by:
Lt = Lt/t-1Lt-1/t-2....L1/0L0
where L0 is some normalized value in period zero. If Eit = Eit-1, this is equivalent to a total
efficiency units series.
In our efficiency unit measure, the assumption that there is no change over time in
efficiency units within any group is dropped. Aggregation in our efficiency units framework is
simple:
Nt = 3Nit = 3Eithit and Nt-1 = 3Nit-1 = 3Eit-1hit-1
so that:
Lt/t-1 = (3Eithit)/3Eit-1hit-1
However, comparison with the composition adjustment approach is easier if a parallel approach
17The March supplement weights were used for all the total estimates.
25
is taken to deal with composition in both cases.
In the BLS approach, the natural logs of the labour input (total efficiency units) ratios for
each group are weighted by the share in total efficiency units:
lnLt/t-1 = 3wit ln(Eithit/Eit-1hit-1) = 3wit ln(hit/hit-1), Eit=Eit-1
By assumption Eit=Eit-1, so it is equivalent to a weighting of the percentage growth in hours of the
groups to get the percentage growth in the composition adjusted total. The equivalent approach to
composition weighting in our efficiency units measure is:
lnLt/t-1 = 3wit ln(Eithit/Eit-1hit-1) = 3witln(Eit/Eit-1)(hit/hit-1)
= 3witln(hit/hit-1) + 3witln(Eit/Eit-1) (5)
The first term in equation (5) is the same as the composition adjusted hours index. However,
there is also a second term which is the weighted sum of the percentage changes in average
efficiency units per hour, or quality, within group. This term is non-zero whenever any group has
a change in average efficiency units per hour over time, i.e. an average quality change via
technological change or selection effects.
Table 6 compares the alternative labour input series estimated using the MCPS. The BLS-
style (Tornqvist) composition adjusted series was calculated as described above, using 120
groups classified by education, age and sex for a population of private paid workers aged 20-64.
An additional composition adjusted series was computed using the Fisher chained index (used in
Canada) instead of the Tornqvist index. The first column reports the aggregate hours estimate
from the MCPS.17 The growth in hours is substantially less than the growth in the composition
26
adjusted hours which are reported in the third and fourth columns. The growth in composition
adjusted hours is itself substantially less than the growth in efficiency units reported in the final
column of Table 6. The same series for the population of all paid workers, 20-64, are reported in
Table 7 and show the same pattern. Composition adjusted hours grow faster than the unadjusted
series because of the increased education level in the population. Efficiency units grow faster
than composition adjusted hours because the composition adjustment ignores technological
change.
The magnitudes of the differences are very large: efficiency units grow almost twice as
fast as hours. The magnitudes of the differences in the growth rates are shown in Table 8.
Unadjusted hours of private sector paid workers for the period 1977 to 2000 has a growth rate of
67.72% ; composition adjusted hours grow by just over 90%. The composition adjustment thus
produces a labour input growth that is about one third higher than the unadjusted hours growth.
However, the growth in efficiency units is 124.42% , which is a labour input growth rate that is
almost 40% higher than the growth rate of composition adjusted hours. The composition
adjustment is therefore less than half of the full adjustment to aggregate hours that is necessary to
estimate labour input growth between 1977 and 2000. The pattern is similar for the full 1975-
2001 period for which efficiency units have been estimated, and for the sample of all paid
workers.
Table 8 also reports the growth rates of alternative labour input measures by sex. The
BLS method for total hours uses compensation shares to weight the growth of each “type” of
hours, including male vs. female. The logic of this weighting suggests that to get separate totals
for males and females, the total labour input estimate should be split between males and females
according to the compensation shares in the year, assuming no discrimination. The results for this
method are denoted BLS (A). An alternative is to apply the BLS method separately to estimate
compensation share weighted male hours growth and compensation share weighted female hours
growth. The results in this case are denoted BLS (B). By construction, the relative rates of growth
in the BLS (B) measures of the labour input by sex simply reflect the relative rates of growth of
27
hours.
Human capital theory predicts that the increased labour market attachment of females has
increased female human capital investment. The substantial literature on female wage
differentials has documented this increase, which has taken many forms, including more market
oriented human capital investments for females at college. This increase has resulted in an
increase in the total labour input of females by all measures, including total hours. Total hours
for female private workers increased by 100.10% from 1977 to 2000, which is double the growth
in male hours of 49.50%. The same pattern occurs for all paid workers: female hours increase by
90.98% and male hours by 42.75%. The growth in efficiency units (EUS) for females, however,
is particularly pronounced. From 1977 to 2000 the growth in efficiency units for females is
211.22%, which is more than double the growth in hours. By contrast, much smaller rates of
growth are estimated using the BLS style measures: 163.93% for BLS (A) and 137.68% for BLS
(B).
The BLS (A) measure for females in Table 8 is closer to the efficiency units increase
because the use of the compensation shares to apportion the total in the BLS (A) case captures
the relative increase for females over time in efficiency units per hour within observed skill cells.
The female growth rates relative to males using BLS (B) by construction reflect the relative rates
of growth of hours. The female growth rates are depressed relative to males. This is a reflection
of the fact that the compensation weighted method cannot adequately capture changes in the
efficiency units per hour of any group. In particular, it is unable to capture the effects of higher
human capital investments of females accompanying the rise in their labour force participation,
including the move to more market oriented human capital investments in their college
education. The same problem occurs more generally, as shown in equation (5) above, for
capturing any overall increase in efficiency units per hour for any group.
The use of compensation shares in the BLS method implicitly assumes that the wage rate
for females reflects the true marginal product, i.e. that there is no discrimination. The estimates
18See the Appendix for more details.
19See Statistics Canada (2001), Appendix 1.
28
of total efficiency units in Tables 6 & 7 are also based on this assumption. If discrimination
creates a significant difference between the wage and the marginal product of female labour,
without adjustment the total efficiency units series would be underestimated, and the degree of
underestimation would vary over time as the degree of discrimination varied. In a standard
employer discrimination model the true efficiency series is calculated separately for males and
females. For males it is calculated as before by dividing total wage payments by the estimated
price; for females, the total wage payments first have to be scaled up according to the amount of
the discrimination.18 If, for example, discrimination against females was 10% in 1975, declining
to zero in 2001, the growth in total efficiency units from 1975 to 2001 for paid workers would
have been 131.25% instead of the 137.40% reported in Table 8.
Aggregate Labour Input Measures for Canada
Statistics Canada takes a similar position to the BLS in recognizing the need to adjust the
aggregate hours measures for composition changes, especially regarding skill levels. The current
methods make use of a very similar chaining technique to that used by the BLS. The Canadian
procedure uses the Fisher ideal index rather than the Tornqvist index. However, as shown in
Tables 6 & 7, these methods produce almost identical estimates. As of 2001, Canada used a two
stage approach, first constructing aggregate hours measures at the industry level, and then
aggregating the hours growth rates at the industry level using weights based on composition
shares. However, an approach similar to that of Jorgenson and the BLS that incorporates
composition adjustment at an earlier stage is being developed.19 The most recent estimates from
this approach are presented in Gu et.al. (2002).
In this section, the alternative estimates of the labour input for Canada are presented.
29
Table 9 reports the estimates for all paid workers for 1980-2000, using the censuses of 1981-
2001. The alternative estimators are the same as for the United States. Columns 1 & 2 report the
unadjusted hours; columns 3 & 4 report composition adjusted hours; and column 5 presents the
efficiency units estimates, using the price series from Section 5. The growth rates are reported in
Table 10, with comparable growth rates for the same period from the United States. The patterns
for Canada are remarkably similar to those for the United States. Table 10 shows that total
unadjusted hours grow faster in the United States, due to the faster growth in hours for males in
the United States. The top half of Table 10 shows that for the United States the growth in total
hours is 46.99% in the United States compared to 40.49% in Canada. The growth in female hours
is slightly higher in Canada (67.09% vs. 63.77%) but male hours grow much slower in Canada
(25.14% vs. 35.73%).
The BLS style composition adjustment to total hours is almost identical in both countries.
In Canada it adjusts total hours upwards by 16.3 percentage points compared to 17.3 in the
United States. The composition adjustments results in estimated rates of growth in the labour
input in both countries that are 36-40% higher compared to unadjusted hours. However, as for
the United States, the composition adjustment in Canada falls a long way short of the growth in
efficiency units. In both countries, the rate of growth of efficiency units is about 40% faster than
the rate of growth of composition adjusted hours.
In the United States the growth rate of efficiency units is 90.11%, which is ten percentage
points higher than Canada’s rate of 79.43%. Roughly two thirds is due to faster growth of hours
in the United States and one third to a faster growth in efficiency units per hour. However, BLS
style comparisons cannot identify the main source of the difference in efficiency units per hour
across countries because only a very small part of the cross country difference in the growth in
efficiency units per hour is due to composition differences.
Aggregate Series in the Business Cycle and Macroeconomics Literature
20Krusell et. al. (2000) use the weights from the year 1980 for the whole period 1964-1993;Kydland and Prescott (1993) use the weights from averaging across all years.
30
In addition to the Jorgenson series and official aggregate labour input measures, other
measures of aggregate input, focusing on composition adjustment, have been constructed in a
variety of studies in the business cycle literature, and the macroeconomics literature generally.
Studies of wage cyclicality, recently reviewed in Bowlus, Liu and Robinson (2002), are
concerned with the effects of a downward “composition bias” on the estimates of the correlation
between wages and the labour input over the cycle. In tackling the problem of composition bias,
these studies implicitly or explicitly construct aggregate wage and hours measures that are
designed to address quality variation in the human capital input over the cycle induced by
composition changes. Examples of these series include Hansen (1993) and Kydland and Prescott
(1993) for a total economy aggregate, and Katz and Murphy (1992) and Krusell et.al. (2000) for
aggregates by skill group. These series are all efficiency units based, either for the economy as a
whole, or within skill group. They all use fixed weights for the entire period, which implicitly
assumes no technological change or selection, and therefore suffer from the same type of bias as
the BLS and Jorgenson estimates, to which they are related.20
To examine the magnitude of the under-estimate of the labour input using the fixed
weight efficiency units methods we constructed efficiency unit aggregates by skill and in total
using a method analogous to Krusell et. al. (2000) and Kydland and Prescott (1989). These fixed
weight methods are similar to the BLS and Jorgenson methods in that they aggregate the hours of
different types of workers using average wages as weights, classifying the different types of
workers according to demographic and other variables such as age, sex and education. While the
BLS and Jorgenson methods use chained indexes of weighted hours growth rates with varying
weights, the fixed weight methods simply compute the hourly efficiency units of a worker of any
given type as the average hourly wage of workers of that type. Applying the fixed weight
efficiency unit method to all workers yields a total labor input in period t of:
It = 3j (WjHjt), j = 1,2,...J
31
where Hjt is total hours of workers of type j in year t, Wj is the average wage of workers of type j
in the reference year ( or averaged over all years), and J is the number of worker types. Similarly,
total labour inputs for particular skills defined by subsets of the J worker types, such as unskilled
(U) and skilled (S) are given by:
Ut = 3j0 U (WjHjt)
and
St = 3j 0 S (WjHjt)
The estimates from the fixed weight methods for the United States are presented in Table
11. The top half of Table 11 reports the estimates for an aggregate labour input across skills. The
rates of growth of hours, efficiency units and the BLS style measure are repeated from Table 8.
The results show that the composition adjustment applied to aggregate hours implied by the fixed
weight approach is almost identical to the BLS style methods and therefore has the same degree
of underestimate of the increase in the labour input.
The lower half of Table 11 reports separate estimates for skilled and unskilled workers,
defined analogously to Krusell et. al. (2000), using weights averaged across years as in Kydland
and Prescott (1989). The results show that within both skill types defined by observed education
level, the fixed weight estimates produce growth rates that are lower than the EUS estimate. The
under-estimate is higher for the skilled group, but even for the unskilled efficiency units grow
almost 30% more than indicated by the fixed weight estimates. Indeed, the fixed weight
estimates differ relatively little from the hours changes, especially for the skilled group. Overall,
the results from Table 11 provide further indication that composition adjustment methods may
substantially under-estimate the rate of growth of the labour input. Fixed weight methods, by
construction, do not permit total efficiency units of labour to increase if the demographic
composition does not change, except through hours. This has little effect for cyclical analysis, but
for longer term secular growth or cross country comparison, it is potentially extremely important.
One important consequence is the potential for serious overestimation of multi-factor
productivity and under-estimation of the role of human capital in growth.
21In the official series for the United States and Canada, MFP is defined in the same way.
22The BLS estimates for labour share in total cost are 0.678 in 1975 and 0.686 in 2001.
32
7. Consequences for Multi-factor Productivity
A major motivation for the construction of “quality” adjusted labour input series like
those of Jorgenson, the BLS and Statistics Canada is that the use of unadjusted hours results in a
substantial bias in the estimation of MFP or TFP.21 Since changes in MFP and TFP are defined
as the residual change in output that cannot be accounted for by the changes in the inputs, the
estimates of these changes depend on the estimates of the changes in the inputs. Define l as the
growth in the true labour input, h as the growth in aggregate hours, and hc as the growth in
composition adjusted hours. Then the over-estimate of the growth in MFP from using h in place
of l is:
sl [l - h]
and the over-estimate of the growth in MFP from using hc in place of l is:
sl [l - hc]
where sl is the share of labour in total costs.
The results in Section 6 indicate that adjusting for composition falls a long way short of a
full quality adjustment, since it cannot capture technological change in human capital production
or increased human capital investment by females. For the United States for the period 1975 to
2001, the growth in hours under-estimates the growth in efficiency units by 70.94 percentage
points. Since the share of labour in total costs is roughly two thirds,22 this implies an over-
estimate of the growth of MFP of almost 50 percentage points. Using composition adjusted hours
under-estimates the growth in efficiency units by 45.46 percentage points, hence this adjustment
still implies an over-estimate of the growth of MFP of over 30 percentage points. The BLS
23See Table PB4a in mfp2ddod.txt at the BLS Multi-factor Productivity website.
24See footnote #3 above.
33
estimate of MFP growth in the private business sector between 1975 and 2001 is 23.76%.23 The
results therefore suggest that all of this is due to an undercount of the increase in the labour input.
For Canada, for the 1980 to 2000 period, efficiency units for paid workers grew by 38.94
percentage points more than unadjusted hours and 22.64 percentage points more than
composition adjusted hours. The labour share of total costs in Canada is similar to that in the
United States at about two thirds. This implies an over-estimate of MFP growth by 15 percentage
points over the 1980 to 2000 period. This is as large as conventional estimates of MFP growth
for the period, suggesting again that all the estimated growth is actually due to an undercount of
the increase in the labour input.
These results for multi-factor productivity indicate that much of the source of
improvement over time in standard of living is due to technological improvements in the
production of human capital. Individuals exposed to more recent education and on-the-job
training systems receive more value added to their human capital. This is not captured by
composition adjustment. In particular, composition adjustment cannot capture a change in the
level of human capital accumulated by college educated workers from the 1966 birth cohort
compared to the level accumulated by an otherwise identical individual from the 1946 birth
cohort.
The results for both countries show an extremely large effect on the estimates of MFP
when quality variation across time in the labour input is controlled for. MFP no longer appears to
be the main driver of within country changes in standard of living. Rather, the main driver
appears to be increases in per capita human capital, adjusted for quality. There is a large and
increasing literature on incorporating quality adjustments to human capital measures for
international comparisons and international growth studies.24 In a recent paper that re-opens the
34
question on the sources of cross country variation in wealth, Manuelli and Seshadri (2005) argue
that quality differences in human capital, that are not captured by observed measures that are
typically used in composition adjustments, substantially reduce the role of MFP or TFP
differences in explaining cross country differences in wealth. Their estimates show very little
cross country difference in TFP when the quality of human capital is taken into account. TFP in
the poorest countries is not much smaller than that of the United States at around 73% of the
United States figure. By contrast, studies that do not take into account human capital quality find
rates for the poorest countries at only 20% of the United States value. These results mirror the
findings in this section that there is little difference across time within countries in MFP when
the quality of human capital is taken into account.
9. Conclusions
Human capital is widely recognized as the most important asset that individuals hold.
Unfortunately, it is not directly observed. As a result previous research has relied on a variety of
proxies based on observable characteristics such as years of schooling. For a variety of purposes,
such as within country variation in wages for a given cohort, these proxies can work quite well
and have formed the basis of thousands of studies. For issues of secular growth, cross country
variation and cross cohort variation in wages, however, they may leave out the most important
source of progress or variation due to technological change in human capital production, broadly
interpreted. In order to estimate this change in the quality of human capital corresponding to a
given observed proxy such as years of schooling, it is necessary to separately identify the price
and the quantity of human capital from the readily available wage observations.
In this paper estimates of human capital prices and quantities are presented for both
Canada and the United States for the same period, and the implications of the estimates for the
sources of growth are examined. The estimated quantity series have important implications for
the source of standard of living improvements in the two countries. The most striking result is
that adjusting the labour input for quality changes by using the estimated quantity series reduces
35
the contribution of MFP growth in standard of living growth to zero. This parallels the recent
result in Manuelli and Seshadri (2005) that quality adjustment to international comparisons of
human capital comes close to eliminating MFP differences as the source of cross country
differences in wealth. The largest part of this quality increase is not due to composition changes
but instead to technological change in human capital production. Since most attempts at adjusting
the labour input for quality changes, such as Krusell et. al. (2000) or the official BLS series used
to estimate MFP, only deal with composition, they cannot capture a large part of the quality
change. While our paper does not provide direct estimates of technological improvement in
human capital production, large differences are found between estimated efficiency units and
composition adjusted hours measures suggesting that technological improvement in human
capital production could be the major source of standard of living growth in the last few decades.
An important result for the analysis of cross country differences in standard of living is
that both prices and quantities of human capital can play significant roles. Much of the
difference in standard of living that opened up between Canada and the United States,
particularly in the 1990's is found to be due to the different paths that the price of human capital
took in the two countries. In particular, while the price of human capital fell in both countries
throughout the 1980's and early 1990's, the price in the United States subsequently began a
substantial recovery, in contrast to the continued decline in Canada. Since the wage a worker
receives is the product of the (rental) price of human capital and the amount of human capital he
or she has for rent, the change in the wage can be decomposed into price and quantity changes.
The average Canadian worker fell behind the average United States worker mainly due to the fall
in the relative price received for the human capital rented, rather than from any deficiency in the
quantity of human capital. It is an interesting topic for future work to examine the relative
importance of price and quantity differences in explaining more general cross country variation
in labour income.
36
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40
TABLE 1
Efficiency Units Price Series for United States, 1975-2001
Standard
Unit
Flat Spot (Dropouts) Flat spot (University) Average
Series
Year Age 46-55 Age 48-57 Age 50-59 Age 53-62
1975 1 1 1 1 1 1
1976 0.9924259 1.02371 1.025424 1.007199 0.995433 1.004095
1977 0.9802408 1.010936 1.004362 1.008081 0.9941186 0.993065
1978 1.020582 1.011398 1.010743 0.9797081 0.9876342 1.005885
1979 0.9609066 0.9640547 0.9745797 0.9462874 0.9750662 0.9697691
1980 0.9179272 0.9314943 0.9346712 0.9158245 0.9090757 0.9204969
1981 0.9015074 0.9215152 0.9336614 0.9154244 0.9039088 0.912473
1982 0.8314961 0.8711348 0.8635144 0.9132852 0.9078457 0.8676744
1983 0.8006828 0.8967901 0.8981088 0.9262186 0.8660981 0.8546029
1984 0.781473 0.8926303 0.8855972 0.9065009 0.8162192 0.8280677
1985 0.7954459 0.8886022 0.8802447 0.8975758 0.84365 0.8398126
1986 0.7550431 0.8852324 0.8726529 0.9237816 0.8770908 0.8353737
1987 0.79483 0.8931988 0.8841341 0.8741345 0.8141932 0.8295785
1988 0.7842304 0.8460958 0.8497909 0.8799793 0.81705 0.8163155
1989 0.8394979 0.8116889 0.8212289 0.8798855 0.8476898 0.8357374
1990 0.7884215 0.7870647 0.811418 0.8318653 0.8284196 0.8107247
1991 0.7496412 0.7698971 0.8016593 0.8182037 0.8158712 0.7874804
1992 0.7470589 0.7829636 0.7958211 0.8092295 0.7998775 0.7812459
1993 0.7359942 0.7524555 0.7682582 0.7951002 0.7826514 0.7609652
1994 0.7478261 0.8121357 0.8264995 0.8159364 0.8063873 0.7922372
1995 0.8047488 0.7736447 0.800245 0.8135469 0.7460631 0.7815578
1996 0.8069699 0.805069 0.7968113 0.7927842 0.7806987 0.7968555
41
1997 0.7703621 0.7689855 0.7602649 0.8113918 0.7977348 0.7756618
1998 0.8196947 0.8000832 0.7855259 0.839236 0.8318172 0.8112343
1999 0.8366837 0.8069197 0.8143474 0.8837759 0.8552672 0.8379319
2000 0.8167102 0.7996168 0.7967138 0.854462 0.8365989 0.8163815
2001 0.838245 0.8228635 0.7992771 0.848218 0.8226217 0.8192139
42
TABLE 2
Efficiency Units Price Series for Canada, 1980-2000
Standard Unit Flat Spot (Dropouts) Flat spot (University) Average
Series
Year Age 19-23 Age 21-25 Age 48-57 Age 49-58 Age 51-60 Age 50-59 Age 51-60 Age 53-62
1980 1 1 1 1 1 1 1 1 1
1985 0.8371 0.8569 0.9491 0.9454 0.9462 0.9647 0.9363 0.9428 0.9474
1990 0.8085 0.8309 0.9265 0.9103 0.9046 0.8883 0.8828 0.9071 0.9031
1995 0.7316 0.7444 0.8782 0.8437 0.808 0.8528 0.8541 0.8476 0.8474
2000 0.7482 0.7464 0.8545 0.8061 0.7604 0.7989 0.7951 0.7686 0.7879
Notes: The sample consists of male paid employees, working mainly full-time last year for 48-52 weeks.
43
Table 3
Rates of Growth in Per Worker Earnings and Efficiency Units:
Paid Workers, 16-64; Canada and the United States, 1980-2000
United States Canada
1980-2000 1990-2000 1980-2000 1990-2000
W&S EUS W&S EUS W&S EUS W&S EUS
PAID
EMPLOYEES 0.2907 0.4554 0.2003 0.192 0.089 0.3822 0.072 0.2291
Males 0.2188 0.3742 0.1971 0.1888 0.037 0.3158 0.048 0.2013
Females 0.5108 0.7035 0.2166 0.2081 0.287 0.6335 0.1318 0.2973
Notes: W&S are wages and salaries; EUS are efficiency units
Table 4
Rates of Growth in Paid Workers and Total Efficiency Units:
Paid Workers, 16-64; Canada and the United States, 1980-2000
United States Canada
1980-2000 1990-2000 1980-2000 1990-2000
POP EUS POP EUS POP EUS POP EUS
PAID
EMPLOYEES 0.2944 0.8838 0.1391 0.3578 0.2872 0.7792 0.092 0.3425
Males 0.2339 0.6957 0.1245 0.3369 0.182 0.5553 0.068 0.2828
Females 0.3647 1.3247 0.1547 0.3951 0.4219 1.3227 0.1195 0.4523
Notes: POP is the population of paid workers, 16-64; EUS are efficiency units
44
TABLE 5
BLS and Jorgenson Composition Adjusted Labor Input Series, 1977-2000
Total Hours (billions) Composition Adjustment Labor Input
Jorgenson BLS Jorgenson BLS Jorgenson Jorgenson* BLS
1977 145.3967 127.413 0.909 0.902 132.129 114.984 114.984
1978 152.4866 133.839 0.91 0.904 138.723 120.752 120.926
1979 157.8711 138.333 0.911 0.901 143.778 125.091 124.597
1980 156.109 137.054 0.909 0.904 141.864 123.453 123.831
1981 157.1794 138.051 0.917 0.91 144.082 125.322 125.645
1982 153.9752 134.803 0.923 0.919 142.061 123.611 123.948
1983 156.7416 137.183 0.924 0.923 144.768 126.022 126.669
1984 165.4984 145.238 0.933 0.924 154.332 134.238 134.262
1985 169.1046 148.597 0.935 0.927 158.03 137.457 137 .7
1986 169.9429 149.594 0.936 0.931 158.982 138.357 139.293
1987 175.6338 154.034 0.941 0.934 165.35 143.807 143.802
1988 180.7782 158.274 0.945 0.941 170.91 148.689 148.93
1989 186.0455 162.533 0.949 0.945 176.628 153.695 153.618
1990 187.2754 161.648 0.958 0.95 179.465 156.175 153.567
1991 183.2378 157.851 0.961 0.961 176.141 153.295 151.664
1992 183.5965 157.69 0.967 0.973 177.577 154.492 153.365
1993 188.5939 162.105 0.976 0.975 184.093 160.263 158.021
1994 194.2605 168.309 0.981 0.98 190.587 165.891 164.937
1995 199.4712 172.948 0.983 0.981 196.095 170.647 169.634
1996 202.7156 175.828 0.991 0.985 200.891 174.805 173.211
1997 209.1744 181.831 0.992 0.991 207.499 180.54 180.116
1998 215.2336 185.709 0.995 0.993 214.15 186.268 184.463
1999 219.4094 189.814 0.997 1 218.739 190.387 189.721
2000 223.0287 191.66 1 1 223.011 194.016 191.66
45
TABLE 6
Comparison of Alternative Labor Input Series, Private Sector: 1977-2000
Unadjusted Hours Composition Adjusted Hours
Total (billions) Index Tornqvist Fisher Efficiency Units
1977 117.7537 108.0142 107.8179 107.8203 110.7096
1978 123.1152 112.9323 112.7404 112.738 114.6653
1979 125.6677 115.2737 114.6705 114.6627 119.8709
1980 129.668 118.9431 118.661 118.6538 125.9492
1981 131.0276 120.1902 120.711 120.7007 125.7318
1982 129.3289 118.6321 120.1273 120.1152 131.1217
1983 132.8805 121.89 123.5739 123.5593 137.0077
1984 140.7109 129.0726 131.5091 131.4955 149.1265
1985 146.9159 134.7644 138.4073 138.3927 156.2929
1986 150.8217 138.3472 142.724 142.704 165.0377
1987 154.1638 141.4129 146.1551 146.1363 169.6338
1988 157.853 144.797 150.7242 150.703 177.1621
1989 160.5897 147.3073 154.4506 154.4276 176.0129
1990 161.7545 148.3758 156.256 156.2293 177.4606
1991 162.2436 148.8244 158.1804 158.1655 181.5416
1992 162.7781 149.3147 160.9345 160.9159 185.1691
1993 165.7894 152.077 165.2209 165.1985 193.1801
1994 171.3907 157.2149 172.2097 172.1854 195.7264
1995 177.688 162.9913 178.8962 178.871 204.8792
1996 180.9425 165.9767 183.1756 183.1424 209.0209
1997 185.6065 170.255 188.9621 188.9233 225.6051
1998 190.6858 174.9142 196.1496 196.1101 228.9369
1999 193.1994 177.2199 200.1184 200.0786 229.5816
2000 197.5009 181.1655 205.178 205.1418 248.4539
Notes: See the Appendix for cell definitions.
46
TABLE 7
Comparison of Alternative Labor Input Series, Paid Workers: 1977-2000
Unadjusted Hours Composition Adjusted Hours
Total Index Tornqvist Fisher Efficiency Units
1977 146.2455 106.5429 106.5563 106.558 109.0206
1978 152.5765 111.1551 111.1707 111.1721 112.242
1979 155.6163 113.3697 113.3093 113.308 117.0975
1980 160.1237 116.6534 116.8424 116.842 122.5305
1981 161.009 117.2984 118.1511 118.1517 121.7774
1982 158.9353 115.7877 117.4353 117.4346 127.073
1983 163.7512 119.2961 121.3482 121.3429 133.5293
1984 172.2239 125.4687 128.1364 128.1326 144.7282
1985 178.1313 129.7723 133.1505 133.1462 150.2028
1986 182.9356 133.2724 137.3454 137.34 158.8784
1987 187.0298 136.2551 140.737 140.7325 163.2148
1988 191.5991 139.5839 145.2336 145.2285 170.614
1989 195.0625 142.1071 148.6597 148.654 170.0605
1990 195.785 142.6334 149.7317 149.7217 171.4322
1991 197.1212 143.6069 152.1546 152.1538 176.5182
1992 198.7658 144.805 155.289 155.2876 180.6833
1993 202.3861 147.4425 159.1748 159.1729 188.7787
1994 208.1018 151.6065 165.1147 165.1094 189.9753
1995 213.127 155.2675 169.105 169.098 196.3288
1996 215.9565 157.3288 171.8405 171.8323 197.7664
1997 221.2122 161.1577 177.0715 177.0609 212.9827
1998 227.0704 165.4255 183.4849 183.4713 215.2639
1999 231.0326 168.3121 187.553 187.5397 216.8229
2000 235.3721 171.4735 191.6503 191.6385 232.9429
Notes: See the Appendix for cell definitions
47
TABLE 8
Comparison of the Growth Rates of Alternative Labour Input Series for the United States
%)1975-2001 %)1977-2000
Private Sector Paid Workers 20-64 (120 cells)
EUS 153.69 124.42
hours 82.75 67.72
BLS 108.33 90.3
Males Females Males Females
EUS 116.03 272.69 95.53 211.22
hours 61.34 122.06 49.5 100.1
BLS (A) 77.42 205.99 65.78 163.93
BLS (B) 88.66 167.4 73.81 137.68
Paid Workers 20-64 (120 cells)
EUS 137.4 113.67
hours 72.83 60.94
BLS 94.31 79.86
Males Females Males Females
EUS 101.61 236.06 85.58 188.63
hours 51.63 108.91 42.75 90.98
BLS (A) 65.03 175.06 56.21 142.93
BLS (B) 74.7 145.88 63.24 122.01
48
TABLE 9
Comparison of Alternative Labor Input Series, Paid Workers: 1980-2000
Unadjusted Hours Composition Adjusted Hours Efficiency
UnitsTotal (billions) Index Tornqvist Fisher
1980 16.5852 100 100 100 100
1985 17.7883 107.2542 109.5616 109.5616 108.7573
1990 20.1829 121.6924 128.0497 127.9724 133.2765
1995 20.3272 122.5624 134.3498 134.2734 139.8786
2000 23.3004 140.4892 156.7929 156.7423 179.4353
Notes: See the Appendix for cell definitions
TABLE 10
Comparison of the Growth Rates of Alternative Labour Input Series:
Paid Workers 20-24, Canada and the United States, 1980-2000
Canada United States
EUS 79.43 90.11
hours 40.49 46.99
BLS 56.79 64.02
Males Females Males Females
EUS 56.25 136.6 70.74 136.04
hours 25.14 67.09 35.73 63.77
BLS (A) 36.51 106.79 47.32 103.61
BLS (B) 40.29 95.74 53.71 86.77
49
TABLE 11
Growth Rates of Fixed Weight Labour Input Series for the United States
%)1975-2001 %)1977-2000
Paid Workers 20-64 (120 cells)
Efficiency Units 137.4 113.67
hours 72.83 60.94
BLS 94.31 79.86
Fixed Weight 94.56 80.21
Skilled Unskilled Skilled Unskilled
Efficiency Units 309.65 76.1 253.99 62.78
hours 173.65 48.52 145.82 40.16
Fixed Weight 184 59.17 152.65 50.77
Notes: See the Appendix for cell definitions.
50
51
52
53
54
55
56
APPENDIX
1. Construction of the Education Groups for Canada
The Canadian censuses for 1981-2001 have a consistent “highest level of schooling”
variable that has three broad groups, “elementary and secondary” (ESS), “Other non-university”
(ONU) and “university” (UNIV) with the following subdivisions:
1 ESS: less than grade 5
2 ESS: grades 5-8
3 ESS: grades 9-13
4 ESS: Secondary graduation certificate
5 ESS: trades certificate/diploma
6 ONU: w/o certificate/diploma
7 ONU: trades certificate/diploma
8 ONU: other non-university certificate/diploma
9 UNIV: w/o certificate/diploma/degree
10 UNIV: with certificate/diploma
11 UNIV : BA or higher
The three groups used in the main analysis in the paper are as follows. The first 3 levels of ESS
have no secondary school graduation certificate or equivalent. These are the “dropout” group.
However, it should be noted that there are also individuals in levels 5-8 without a secondary
school graduation certificate or equivalent. The levels 4-10 are the “other” group. Level 11 is the
BA degree or higher group.
2. Discrimination and Female Efficiency Units
Calculation of efficiency units for females depends on whether the male-female wage
differential is due to human capital differences or employer discrimination. The differential has
57
narrowed over the 1975 to 2001 period, either because discrimination decreased, or because
female human capital relative to males, increased within cells. In the latter case, female human
capital may have been less market oriented in the earlier data period, when the female
participation rate was low.
The estimated price series were obtained from male samples. If the male-female
differences are all human capital differences, the same price series applies to females, and males
and females with the same wage have the same amount of human capital. This assumption was
used as the benchmark for the quantity estimates in section 6. If the male female differences are
due to discrimination, the efficiency units reported for females (and hence the totals) should be
adjusted downward. The simplest case is where employers have the same discrimination
coefficient. In that case, the psychic cost of employing a female efficiency unit will exactly offset
in the wage. Thus, the “total” price for a female efficiency unit to an employer will be the same
as that for a male efficiency unit. However, while the male efficiency units follow from dividing
the total expenditure on males by this price, the female efficiency units do not.
Suppose the dollar price 8m is paid for a standard male unit and 8f for the same level of
human capital for a female, with the additional psychic cost of (8m - 8f ) also paid by the
employer of the female due to discrimination. Female efficiency units then follow from dividing
total dollar payments to females by 8f . The benchmark procedure in Section 6 will under-
estimate the female efficiency units in any period by the percentage difference between 8m and 8f
in the period. Thus if discrimination falls over time, the growth in female efficiency units over
the period will be over-estimated.
3. Cell Definitions Used in the Composition Adjusted Series
The BLS and Jorgenson series, based on chained weighted rates of growth different
workers hours, and the fixed weight series that compute weighted aggregates of hours of
different workers, use cells based on demographic and other characteristics of the workers such
58
as age, education and sex. The analysis in Section 6 uses the same cell definitions for all
composition adjusted series. These consist of 120 cells obtained from the four education levels
defined in Section 3, by fifteen 3-year age categories from 20 to 64, by males and females.
Experimentation with cell definition and coverage indicates that the results are insensitive to the
precise cell definitions.
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